LMFDB - Embedded newform 869.1.j.a.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [869,1,Mod(157,869)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(869, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 5]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("869.157");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 869 = 11 \cdot 79 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	869.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.433687495978$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{25}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{25} - \cdots)$

Embedding invariants

Embedding label			157.3
Root			$-0.968583 + 0.248690i$ of defining polynomial
Character	$\chi$	$=$	869.157
Dual form			869.1.j.a.631.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.183089 q^{10} +(0.0627905 - 0.998027i) q^{11} +(-1.56720 + 1.13864i) q^{13} +(-0.770942 - 0.560122i) q^{16} +(0.0388067 - 0.119435i) q^{18} +(-0.263146 - 0.809880i) q^{19} +(1.16089 - 0.843439i) q^{20} +(0.0672897 + 0.106032i) q^{22} -0.851559 q^{23} +(0.347824 + 1.07049i) q^{25} +(0.0751750 - 0.231365i) q^{26} +(-0.866986 + 0.629902i) q^{31} +0.368852 q^{32} +(-0.304144 - 0.936058i) q^{36} +(0.0865160 + 0.0628575i) q^{38} +(-0.112263 + 0.345510i) q^{40} +(0.915113 + 0.362319i) q^{44} +1.45794 q^{45} +(0.0865160 - 0.0628575i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-0.114356 - 0.0830844i) q^{50} +(-0.589177 - 1.81330i) q^{52} +(-0.929324 + 1.12336i) q^{55} +(0.0415873 - 0.127993i) q^{62} +(0.733468 - 0.532896i) q^{64} +2.82427 q^{65} +1.75261 q^{67} +(0.201592 + 0.146465i) q^{72} +(-0.613161 + 1.88711i) q^{73} +0.838129 q^{76} +(-0.809017 + 0.587785i) q^{79} +(0.429324 + 1.32132i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(-0.241353 + 0.0619689i) q^{88} -1.85955 q^{89} +(-0.148122 + 0.107617i) q^{90} +(0.258996 - 0.797108i) q^{92} +(-0.383650 + 1.18075i) q^{95} +(0.303189 - 0.220280i) q^{97} +0.125581 q^{98} +(0.535827 + 0.844328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^4 - 5 * q^9	$ 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} + 15 q^{20} - 5 q^{22} - 5 q^{25} + 15 q^{26} - 10 q^{32} - 5 q^{36} - 10 q^{40} - 5 q^{49} - 10 q^{50} - 10 q^{62} - 5 q^{64} - 10 q^{76} - 5 q^{79} - 10 q^{80} - 5 q^{81} + 15 q^{83} - 5 q^{88} + 15 q^{92} + 15 q^{95}+O(q^{100}) $ 20 * q - 5 * q^4 - 5 * q^9 - 5 * q^16 + 15 * q^20 - 5 * q^22 - 5 * q^25 + 15 * q^26 - 10 * q^32 - 5 * q^36 - 10 * q^40 - 5 * q^49 - 10 * q^50 - 10 * q^62 - 5 * q^64 - 10 * q^76 - 5 * q^79 - 10 * q^80 - 5 * q^81 + 15 * q^83 - 5 * q^88 + 15 * q^92 + 15 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/869\mathbb{Z}\right)^\times$.

$n$	$475$	$793$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	−0.637424	−	0.770513i	$-0.720000\pi$
$2$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	0.535827	+	0.844328i	$0.320000\pi$
$3$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$3$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$4$	−0.304144	+	0.936058i	−0.304144	+	0.936058i
$5$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$5$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$6$		0			0
$7$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$7$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$8$	−0.0770013	−	0.236986i	−0.0770013	−	0.236986i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$	0.183089			0.183089
$11$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$11$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$12$		0			0
$13$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$13$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$14$		0			0
$15$		0			0
$16$	−0.770942	−	0.560122i	−0.770942	−	0.560122i
$17$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$17$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$18$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$19$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$19$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$20$	1.16089	−	0.843439i	1.16089	−	0.843439i
$21$		0			0
$22$	0.0672897	+	0.106032i	0.0672897	+	0.106032i
$23$	−0.851559			−0.851559			−0.425779	−	0.904827i	$-0.640000\pi$
$23$	−0.851559			−0.851559			−0.425779	+	0.904827i	$0.640000\pi$
$24$		0			0
$25$	0.347824	+	1.07049i	0.347824	+	1.07049i
$26$	0.0751750	−	0.231365i	0.0751750	−	0.231365i
$27$		0			0
$28$		0			0
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$		0			0
$31$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	−0.929776	−	0.368125i	$-0.880000\pi$
$31$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$32$	0.368852			0.368852
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.304144	−	0.936058i	−0.304144	−	0.936058i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	0.0865160	+	0.0628575i	0.0865160	+	0.0628575i
$39$		0			0
$40$	−0.112263	+	0.345510i	−0.112263	+	0.345510i
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	0.915113	+	0.362319i	0.915113	+	0.362319i
$45$	1.45794			1.45794
$46$	0.0865160	−	0.0628575i	0.0865160	−	0.0628575i
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$50$	−0.114356	−	0.0830844i	−0.114356	−	0.0830844i
$51$		0			0
$52$	−0.589177	−	1.81330i	−0.589177	−	1.81330i
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$		0			0
$55$	−0.929324	+	1.12336i	−0.929324	+	1.12336i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$		0			0
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$	0.0415873	−	0.127993i	0.0415873	−	0.127993i
$63$		0			0
$64$	0.733468	−	0.532896i	0.733468	−	0.532896i
$65$	2.82427			2.82427
$66$		0			0
$67$	1.75261			1.75261			0.876307	−	0.481754i	$-0.160000\pi$
$67$	1.75261			1.75261			0.876307	+	0.481754i	$0.160000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	0.201592	+	0.146465i	0.201592	+	0.146465i
$73$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$73$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$74$		0			0
$75$		0			0
$76$	0.838129			0.838129
$77$		0			0
$78$		0			0
$79$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$79$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$80$	0.429324	+	1.32132i	0.429324	+	1.32132i
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$		0			0
$83$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$83$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.241353	+	0.0619689i	−0.241353	+	0.0619689i
$89$	−1.85955			−1.85955			−0.929776	−	0.368125i	$-0.880000\pi$
$89$	−1.85955			−1.85955			−0.929776	+	0.368125i	$0.880000\pi$
$90$	−0.148122	+	0.107617i	−0.148122	+	0.107617i
$91$		0			0
$92$	0.258996	−	0.797108i	0.258996	−	0.797108i
$93$		0			0
$94$		0			0
$95$	−0.383650	+	1.18075i	−0.383650	+	1.18075i
$96$		0			0
$97$	0.303189	−	0.220280i	0.303189	−	0.220280i	−0.425779	−	0.904827i	$-0.640000\pi$
$97$	0.303189	−	0.220280i	0.303189	−	0.220280i	0.728969	+	0.684547i	$0.240000\pi$
$98$	0.125581			0.125581
$99$	0.535827	+	0.844328i	0.535827	+	0.844328i
$100$	−1.10783			−1.10783
$101$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$101$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	0.390518	+	0.283728i	0.390518	+	0.283728i
$105$		0			0
$106$		0			0
$107$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$107$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	0.0114963	−	0.182728i	0.0114963	−	0.182728i
$111$		0			0
$112$		0			0
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$	1.00441	+	0.729747i	1.00441	+	0.729747i
$116$		0			0
$117$	0.598617	−	1.84235i	0.598617	−	1.84235i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$122$		0			0
$123$		0			0
$124$	−0.325937	−	1.00313i	−0.325937	−	1.00313i
$125$	0.0565777	−	0.174128i	0.0565777	−	0.174128i
$126$		0			0
$127$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$127$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$128$	−0.149164	+	0.459081i	−0.149164	+	0.459081i
$129$		0			0
$130$	−0.286938	+	0.208472i	−0.286938	+	0.208472i
$131$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$131$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$132$		0			0
$133$		0			0
$134$	−0.178061	+	0.129369i	−0.178061	+	0.129369i
$135$		0			0
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.03799	+	1.63560i	1.03799	+	1.63560i
$144$	0.952937			0.952937
$145$		0			0
$146$	−0.0770013	−	0.236986i	−0.0770013	−	0.236986i
$147$		0			0
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$		0			0
$151$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$151$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$152$	−0.171668	+	0.124724i	−0.171668	+	0.124724i
$153$		0			0
$154$		0			0
$155$	1.56240			1.56240
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$159$		0			0
$160$	−0.435060	−	0.316090i	−0.435060	−	0.316090i
$161$		0			0
$162$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$163$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$163$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$164$		0			0
$165$		0			0
$166$	−0.203194			−0.203194
$167$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	−0.929776	−	0.368125i	$-0.880000\pi$
$167$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$168$		0			0
$169$	0.850604	−	2.61789i	0.850604	−	2.61789i
$170$		0			0
$171$	0.688925	+	0.500534i	0.688925	+	0.500534i
$172$		0			0
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		0			0
$176$	−0.607425	+	0.734251i	−0.607425	+	0.734251i
$177$		0			0
$178$	0.188925	−	0.137262i	0.188925	−	0.137262i
$179$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$179$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$180$	−0.443422	+	1.36471i	−0.443422	+	1.36471i
$181$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.929776	−	0.368125i	$-0.880000\pi$
$181$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.637424	−	0.770513i	$-0.720000\pi$
$182$		0			0
$183$		0			0
$184$	0.0655712	+	0.201807i	0.0655712	+	0.201807i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.0481792	−	0.148280i	−0.0481792	−	0.148280i
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$		0			0
$193$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$193$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$194$	−0.0145433	+	0.0447596i	−0.0145433	+	0.0447596i
$195$		0			0
$196$	0.796258	−	0.578516i	0.796258	−	0.578516i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	0.226908	−	0.164859i	0.226908	−	0.164859i
$201$		0			0
$202$	−0.0721631	+	0.222095i	−0.0721631	+	0.222095i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.688925	−	0.500534i	0.688925	−	0.500534i
$208$	1.84600			1.84600
$209$	−0.824805	+	0.211774i	−0.824805	+	0.211774i
$210$		0			0
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.768882	−	1.21156i	−0.768882	−	1.21156i
$221$		0			0
$222$		0			0
$223$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$223$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$224$		0			0
$225$	−0.910614	−	0.661600i	−0.910614	−	0.661600i
$226$		0			0
$227$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$229$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$230$	−0.155911			−0.155911
$231$		0			0
$232$		0			0
$233$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$233$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$234$	0.0751750	+	0.231365i	0.0751750	+	0.231365i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$239$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$240$		0			0
$241$	−1.27485			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$241$	−1.27485			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$242$	0.110048	−	0.0604991i	0.110048	−	0.0604991i
$243$		0			0
$244$		0			0
$245$	0.450527	+	1.38658i	0.450527	+	1.38658i
$246$		0			0
$247$	1.33456	+	0.969617i	1.33456	+	0.969617i
$248$	0.216037	+	0.156960i	0.216037	+	0.156960i
$249$		0			0
$250$	0.00710509	+	0.0218672i	0.00710509	+	0.0218672i
$251$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i
$254$		0			0
$255$		0			0
$256$	0.261428	+	0.804591i	0.261428	+	0.804591i
$257$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$257$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.535827	−	0.844328i	$-0.320000\pi$
$258$		0			0
$259$		0			0
$260$	−0.858983	+	2.64368i	−0.858983	+	2.64368i
$261$		0			0
$262$	0.201592	−	0.146465i	0.201592	−	0.146465i
$263$	−1.27485			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$263$	−1.27485			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.533046	+	1.64055i	−0.533046	+	1.64055i
$269$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$269$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$270$		0			0
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.09022	−	0.279921i	1.09022	−	0.279921i
$276$		0			0
$277$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$277$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$278$		0			0
$279$	0.331159	−	1.01920i	0.331159	−	1.01920i
$280$		0			0
$281$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$281$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$282$		0			0
$283$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$283$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$284$		0			0
$285$		0			0
$286$	−0.226188	−	0.0895542i	−0.226188	−	0.0895542i
$287$		0			0
$288$	−0.298408	+	0.216806i	−0.298408	+	0.216806i
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$	−1.57996	−	1.14791i	−1.57996	−	1.14791i
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.33456	−	0.969617i	1.33456	−	0.969617i
$300$		0			0
$301$		0			0
$302$	−0.178061	−	0.129369i	−0.178061	−	0.129369i
$303$		0			0
$304$	−0.250762	+	0.771765i	−0.250762	+	0.771765i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−0.158736	+	0.115328i	−0.158736	+	0.115328i
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$313$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$314$		0			0
$315$		0			0
$316$	−0.304144	−	0.936058i	−0.304144	−	0.936058i
$317$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$317$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$		0			0
$320$	−1.32179			−1.32179
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.796258	+	0.578516i	0.796258	+	0.578516i
$325$	−1.76401	−	1.28163i	−1.76401	−	1.28163i
$326$	−0.0494726	+	0.152261i	−0.0494726	+	0.152261i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−1.28837	+	0.936058i	−1.28837	+	0.936058i
$333$		0			0
$334$	0.0415873	−	0.127993i	0.0415873	−	0.127993i
$335$	−2.06720	−	1.50191i	−2.06720	−	1.50191i
$336$		0			0
$337$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	−0.992115	−	0.125333i	$-0.960000\pi$
$337$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	0.876307	+	0.481754i	$0.160000\pi$
$338$	0.106820	+	0.328757i	0.106820	+	0.328757i
$339$		0			0
$340$		0			0
$341$	0.574221	+	0.904827i	0.574221	+	0.904827i
$342$	−0.106940			−0.106940
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$347$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$348$		0			0
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$		0			0
$351$		0			0
$352$	0.0231604	−	0.368125i	0.0231604	−	0.368125i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$	0.565571	−	1.74065i	0.565571	−	1.74065i
$357$		0			0
$358$	0.164388	+	0.119435i	0.164388	+	0.119435i
$359$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$359$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$360$	−0.112263	−	0.345510i	−0.112263	−	0.345510i
$361$	0.222357	−	0.161552i	0.222357	−	0.161552i
$362$	0.243271			0.243271
$363$		0			0
$364$		0			0
$365$	2.34039	−	1.70039i	2.34039	−	1.70039i
$366$		0			0
$367$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$367$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$368$	0.656502	+	0.476977i	0.656502	+	0.476977i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$	−0.988570	−	0.718238i	−0.988570	−	0.718238i
$381$		0			0
$382$		0			0
$383$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	−0.637424	−	0.770513i	$-0.720000\pi$
$383$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	0.535827	+	0.844328i	$0.320000\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.113982	+	0.350799i	0.113982	+	0.350799i
$389$	0.331159	−	1.01920i	0.331159	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$389$	0.331159	−	1.01920i	0.331159	−	1.01920i	0.968583	−	0.248690i	$-0.0800000\pi$
$390$		0			0
$391$		0			0
$392$	−0.0770013	+	0.236986i	−0.0770013	+	0.236986i
$393$		0			0
$394$		0			0
$395$	1.45794			1.45794
$396$	−0.953308	+	0.244768i	−0.953308	+	0.244768i
$397$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$397$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$	0.331454	−	1.02011i	0.331454	−	1.02011i
$401$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$401$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$402$		0			0
$403$	0.641510	−	1.97437i	0.641510	−	1.97437i
$404$	0.565571	+	1.74065i	0.565571	+	1.74065i
$405$	−1.17950	+	0.856954i	−1.17950	+	0.856954i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$409$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.0330462	+	0.101706i	−0.0330462	+	0.101706i
$415$	−0.728969	−	2.24353i	−0.728969	−	2.24353i
$416$	−0.578066	+	0.419989i	−0.578066	+	0.419989i
$417$		0			0
$418$	0.0681659	−	0.0823984i	0.0681659	−	0.0823984i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$421$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.728969	−	0.684547i	$-0.240000\pi$
$431$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$432$		0			0
$433$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	0.728969	+	0.684547i	$0.240000\pi$
$433$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.224084	+	0.689661i	0.224084	+	0.689661i
$438$		0			0
$439$	−0.374763			−0.374763			−0.187381	−	0.982287i	$-0.560000\pi$
$439$	−0.374763			−0.374763			−0.187381	+	0.982287i	$0.560000\pi$
$440$	0.337780	+	0.133736i	0.337780	+	0.133736i
$441$	1.00000			1.00000
$442$		0			0
$443$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$443$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$	2.19334	+	1.59355i	2.19334	+	1.59355i
$446$	0.164388	+	0.119435i	0.164388	+	0.119435i
$447$		0			0
$448$		0			0
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$	0.141352			0.141352
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$457$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$458$		0			0
$459$		0			0
$460$	−0.988570	+	0.718238i	−0.988570	+	0.718238i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$467$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$468$	1.54248	+	1.12068i	1.54248	+	1.12068i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.775441	−	0.563391i	0.775441	−	0.563391i
$476$		0			0
$477$		0			0
$478$	−0.148122	−	0.107617i	−0.148122	−	0.107617i
$479$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$479$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$480$		0			0
$481$		0			0
$482$	0.129521	−	0.0941025i	0.129521	−	0.0941025i
$483$		0			0
$484$	0.419064	−	0.890557i	0.419064	−	0.890557i
$485$	−0.546380			−0.546380
$486$		0			0
$487$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$487$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.0627905	+	0.998027i	$0.480000\pi$
$488$		0			0
$489$		0			0
$490$	−0.148122	−	0.107617i	−0.148122	−	0.107617i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$	−0.207160			−0.207160
$495$	0.0915446	−	1.45506i	0.0915446	−	1.45506i
$496$	1.02122			1.02122
$497$		0			0
$498$		0			0
$499$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	−0.929776	−	0.368125i	$-0.880000\pi$
$499$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	0.968583	+	0.248690i	$0.0800000\pi$
$500$	0.145786	+	0.105920i	0.145786	+	0.105920i
$501$		0			0
$502$		0			0
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$	−2.71111			−2.71111
$506$	−0.0573011	−	0.0902921i	−0.0573011	−	0.0902921i
$507$		0			0
$508$		0			0
$509$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$509$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	−0.476468	−	0.346175i	−0.476468	−	0.346175i
$513$		0			0
$514$	0.0751750	+	0.231365i	0.0751750	+	0.231365i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.217472	−	0.669311i	−0.217472	−	0.669311i
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$		0			0
$523$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$523$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$524$	0.603491	−	1.85735i	0.603491	−	1.85735i
$525$		0			0
$526$	0.129521	−	0.0941025i	0.129521	−	0.0941025i
$527$		0			0
$528$		0			0
$529$	−0.274848			−0.274848
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.134954	−	0.415344i	−0.134954	−	0.415344i
$537$		0			0
$538$	0.220095			0.220095
$539$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$540$		0			0
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$547$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$548$		0			0
$549$		0			0
$550$	−0.0901009	+	0.108913i	−0.0901009	+	0.108913i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.0565777	−	0.174128i	0.0565777	−	0.174128i
$555$		0			0
$556$		0			0
$557$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	0.728969	+	0.684547i	$0.240000\pi$
$557$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	−0.992115	+	0.125333i	$0.960000\pi$
$558$	0.0415873	+	0.127993i	0.0415873	+	0.127993i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.183089			0.183089
$563$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$563$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$	−0.108877	−	0.0791038i	−0.108877	−	0.0791038i
$567$		0			0
$568$		0			0
$569$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$569$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$570$		0			0
$571$	1.07165			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$571$	1.07165			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$572$	−1.84672	+	0.474156i	−1.84672	+	0.474156i
$573$		0			0
$574$		0			0
$575$	−0.296192	−	0.911586i	−0.296192	−	0.911586i
$576$	−0.280160	+	0.862243i	−0.280160	+	0.862243i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.494433			0.494433
$585$	−2.28488	+	1.66006i	−2.28488	+	1.66006i
$586$		0			0
$587$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$587$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$588$		0			0
$589$	0.738289	+	0.536399i	0.738289	+	0.536399i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.45794			1.45794			0.728969	−	0.684547i	$-0.240000\pi$
$593$	1.45794			1.45794			0.728969	+	0.684547i	$0.240000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.0640159	+	0.197021i	−0.0640159	+	0.197021i
$599$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$599$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$600$		0			0
$601$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$601$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$602$		0			0
$603$	−1.41789	+	1.03016i	−1.41789	+	1.03016i
$604$	−1.72497			−1.72497
$605$	1.06279	+	0.998027i	1.06279	+	0.998027i
$606$		0			0
$607$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$607$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$608$	−0.0970621	−	0.298726i	−0.0970621	−	0.298726i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$613$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.93717			1.93717			0.968583	−	0.248690i	$-0.0800000\pi$
$617$	1.93717			1.93717			0.968583	+	0.248690i	$0.0800000\pi$
$618$		0			0
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$	−0.475195	+	1.46250i	−0.475195	+	1.46250i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.694661	−	0.504701i	0.694661	−	0.504701i
$626$	0.134579			0.134579
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$	0.201592	+	0.146465i	0.201592	+	0.146465i
$633$		0			0
$634$	0.0239838	−	0.0738147i	0.0239838	−	0.0738147i
$635$		0			0
$636$		0			0
$637$	1.93717			1.93717
$638$		0			0
$639$		0			0
$640$	0.569350	−	0.413657i	0.569350	−	0.413657i
$641$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$641$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$642$		0			0
$643$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$643$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	−0.249182			−0.249182
$649$		0			0
$650$	0.273822			0.273822
$651$		0			0
$652$	0.387737	+	1.19333i	0.387737	+	1.19333i
$653$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$653$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$654$		0			0
$655$	2.34039	+	1.70039i	2.34039	+	1.70039i
$656$		0			0
$657$	−0.613161	−	1.88711i	−0.613161	−	1.88711i
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	0.124591	−	0.383451i	0.124591	−	0.383451i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.325937	−	1.00313i	−0.325937	−	1.00313i
$669$		0			0
$670$	0.320885			0.320885
$671$		0			0
$672$		0			0
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$	−0.0145433	−	0.0447596i	−0.0145433	−	0.0447596i
$675$		0			0
$676$	2.19179	+	1.59243i	2.19179	+	1.59243i
$677$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$677$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−0.125129	−	0.0495420i	−0.125129	−	0.0495420i
$683$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$683$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$684$	−0.678061	+	0.492640i	−0.678061	+	0.492640i
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$		0			0
$693$		0			0
$694$	0.220095			0.220095
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$701$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$702$		0			0
$703$		0			0
$704$	−0.485789	−	0.765481i	−0.485789	−	0.765481i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$	0.309017	−	0.951057i	0.309017	−	0.951057i
$712$	0.143188	+	0.440688i	0.143188	+	0.440688i
$713$	0.738289	−	0.536399i	0.738289	−	0.536399i
$714$		0			0
$715$	0.177337	−	2.81869i	0.177337	−	2.81869i
$716$	1.59252			1.59252
$717$		0			0
$718$		0			0
$719$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	0.535827	+	0.844328i	$0.320000\pi$
$719$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	−0.929776	+	0.368125i	$0.880000\pi$
$720$	−1.12399	−	0.816623i	−1.12399	−	0.816623i
$721$		0			0
$722$	−0.0106659	+	0.0328264i	−0.0106659	+	0.0328264i
$723$		0			0
$724$	1.54248	−	1.12068i	1.54248	−	1.12068i
$725$		0			0
$726$		0			0
$727$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$727$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$	−0.112263	+	0.345510i	−0.112263	+	0.345510i
$731$		0			0
$732$		0			0
$733$	0.541587	−	1.66683i	0.541587	−	1.66683i	−0.187381	−	0.982287i	$-0.560000\pi$
$733$	0.541587	−	1.66683i	0.541587	−	1.66683i	0.728969	−	0.684547i	$-0.240000\pi$
$734$	−0.0721631	−	0.222095i	−0.0721631	−	0.222095i
$735$		0			0
$736$	−0.314099			−0.314099
$737$	0.110048	−	1.74915i	0.110048	−	1.74915i
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.929776	−	0.368125i	$-0.880000\pi$
$743$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.637424	−	0.770513i	$-0.720000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.61803			−1.61803
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	0.968583	−	0.248690i	$-0.0800000\pi$
$751$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	−0.929776	+	0.368125i	$0.880000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.789600	−	2.43014i	0.789600	−	2.43014i
$756$		0			0
$757$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$757$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$758$		0			0
$759$		0			0
$760$	0.309364			0.309364
$761$	0.688925	−	0.500534i	0.688925	−	0.500534i	−0.187381	−	0.982287i	$-0.560000\pi$
$761$	0.688925	−	0.500534i	0.688925	−	0.500534i	0.876307	+	0.481754i	$0.160000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.00487338	−	0.0149987i	0.00487338	−	0.0149987i
$767$		0			0
$768$		0			0
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.613161	−	1.88711i	−0.613161	−	1.88711i	−0.425779	−	0.904827i	$-0.640000\pi$
$773$	−0.613161	−	1.88711i	−0.613161	−	1.88711i	−0.187381	−	0.982287i	$-0.560000\pi$
$774$		0			0
$775$	−0.975863	−	0.709006i	−0.975863	−	0.709006i
$776$	−0.0755492	−	0.0548897i	−0.0755492	−	0.0548897i
$777$		0			0
$778$	0.0415873	+	0.127993i	0.0415873	+	0.127993i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.294474	+	0.906297i	0.294474	+	0.906297i
$785$		0			0
$786$		0			0
$787$	0.303189	+	0.220280i	0.303189	+	0.220280i	0.728969	−	0.684547i	$-0.240000\pi$
$787$	0.303189	+	0.220280i	0.303189	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$788$		0			0
$789$		0			0
$790$	−0.148122	+	0.107617i	−0.148122	+	0.107617i
$791$		0			0
$792$	0.158834	−	0.191998i	0.158834	−	0.191998i
$793$		0			0
$794$	0.164388	−	0.119435i	0.164388	−	0.119435i
$795$		0			0
$796$		0			0
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$	0.128296	+	0.394853i	0.128296	+	0.394853i
$801$	1.50441	−	1.09302i	1.50441	−	1.09302i
$802$		0			0
$803$	1.84489	+	0.730444i	1.84489	+	0.730444i
$804$		0			0
$805$		0			0
$806$	0.0805615	+	0.247943i	0.0805615	+	0.247943i
$807$		0			0
$808$	−0.374871	−	0.272360i	−0.374871	−	0.272360i
$809$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$809$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$810$	0.0565777	−	0.174128i	0.0565777	−	0.174128i
$811$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$811$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.85865			−1.85865
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.331159	−	1.01920i	0.331159	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$821$	0.331159	−	1.01920i	0.331159	−	1.01920i	0.968583	−	0.248690i	$-0.0800000\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$	0.258996	+	0.797108i	0.258996	+	0.797108i
$829$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$829$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$830$	0.239667	+	0.174128i	0.239667	+	0.174128i
$831$		0			0
$832$	−0.542716	+	1.67031i	−0.542716	+	1.67031i
$833$		0			0
$834$		0			0
$835$	1.56240			1.56240
$836$	0.0526266	−	0.836475i	0.0526266	−	0.836475i
$837$		0			0
$838$		0			0
$839$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$839$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$840$		0			0
$841$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$842$	0.0380748	+	0.0276630i	0.0380748	+	0.0276630i
$843$		0			0
$844$		0			0
$845$	−3.24670	+	2.35886i	−3.24670	+	2.35886i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$	−0.383650	−	1.18075i	−0.383650	−	1.18075i
$856$		0			0
$857$	−0.851559			−0.851559			−0.425779	−	0.904827i	$-0.640000\pi$
$857$	−0.851559			−0.851559			−0.425779	+	0.904827i	$0.640000\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	−0.0770013	+	0.236986i	−0.0770013	+	0.236986i
$863$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$863$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$864$		0			0
$865$		0			0
$866$	−0.0330462	−	0.101706i	−0.0330462	−	0.101706i
$867$		0			0
$868$		0			0
$869$	0.535827	+	0.844328i	0.535827	+	0.844328i
$870$		0			0
$871$	−2.74670	+	1.99559i	−2.74670	+	1.99559i
$872$		0			0
$873$	−0.115808	+	0.356420i	−0.115808	+	0.356420i
$874$	−0.0736734	−	0.0535269i	−0.0736734	−	0.0535269i
$875$		0			0
$876$		0			0
$877$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$877$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$878$	0.0380748	−	0.0276630i	0.0380748	−	0.0276630i
$879$		0			0
$880$	1.34567	−	0.345510i	1.34567	−	0.345510i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.450527	−	1.38658i	0.450527	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$887$	0.450527	−	1.38658i	0.450527	−	1.38658i	0.876307	−	0.481754i	$-0.160000\pi$
$888$		0			0
$889$		0			0
$890$	−0.340464			−0.340464
$891$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$892$	1.59252			1.59252
$893$		0			0
$894$		0			0
$895$	−0.728969	+	2.24353i	−0.728969	+	2.24353i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.896253	−	0.651166i	0.896253	−	0.651166i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.872746	+	2.68604i	0.872746	+	2.68604i
$906$		0			0
$907$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$907$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$908$		0			0
$909$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$910$		0			0
$911$	−1.41789	+	1.03016i	−1.41789	+	1.03016i	−0.425779	+	0.904827i	$0.640000\pi$
$911$	−1.41789	+	1.03016i	−1.41789	+	1.03016i	−0.992115	+	0.125333i	$0.960000\pi$
$912$		0			0
$913$	1.03137	−	1.24672i	1.03137	−	1.24672i
$914$	−0.233525			−0.233525
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$919$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$920$	0.0955986	−	0.294222i	0.0955986	−	0.294222i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$		0			0
$931$	−0.263146	+	0.809880i	−0.263146	+	0.809880i
$932$		0			0
$933$		0			0
$934$	0.0157706			0.0157706
$935$		0			0
$936$	−0.482706			−0.482706
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$941$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	−1.18779	−	3.65565i	−1.18779	−	3.65565i
$950$	−0.0371961	+	0.114478i	−0.0371961	+	0.114478i
$951$		0			0
$952$		0			0
$953$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	0.535827	+	0.844328i	$0.320000\pi$
$953$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	−0.929776	+	0.368125i	$0.880000\pi$
$954$		0			0
$955$		0			0
$956$	−1.43494			−1.43494
$957$		0			0
$958$	−0.203194			−0.203194
$959$		0			0
$960$		0			0
$961$	0.0458709	−	0.141176i	0.0458709	−	0.141176i
$962$		0			0
$963$		0			0
$964$	0.387737	−	1.19333i	0.387737	−	1.19333i
$965$		0			0
$966$		0			0
$967$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$968$	0.0466920	+	0.244768i	0.0466920	+	0.244768i
$969$		0			0
$970$	0.0555107	−	0.0403309i	0.0555107	−	0.0403309i
$971$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$971$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$972$		0			0
$973$		0			0
$974$	−0.196811	−	0.142991i	−0.196811	−	0.142991i
$975$		0			0
$976$		0			0
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$	−0.116762	+	1.85588i	−0.116762	+	1.85588i
$980$	−1.43494			−1.43494
$981$		0			0
$982$		0			0
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−1.31352	+	0.954325i	−1.31352	+	0.954325i
$989$		0			0
$990$	0.0981041	+	0.154587i	0.0981041	+	0.154587i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.319790	+	0.232341i	−0.319790	+	0.232341i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.541587	−	1.66683i	0.541587	−	1.66683i	−0.187381	−	0.982287i	$-0.560000\pi$
$997$	0.541587	−	1.66683i	0.541587	−	1.66683i	0.728969	−	0.684547i	$-0.240000\pi$
$998$	0.00487338	+	0.0149987i	0.00487338	+	0.0149987i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	869.1.j.a.157.3	✓	20
11.4	even	5	inner	869.1.j.a.631.3	yes	20
79.78	odd	2	CM	869.1.j.a.157.3	✓	20
869.631	odd	10	inner	869.1.j.a.631.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
869.1.j.a.157.3	✓	20	1.1	even	1	trivial
869.1.j.a.157.3	✓	20	79.78	odd	2	CM
869.1.j.a.631.3	yes	20	11.4	even	5	inner
869.1.j.a.631.3	yes	20	869.631	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 869 = 11 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	869.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.183089 q^{10} +(0.0627905 - 0.998027i) q^{11} +(-1.56720 + 1.13864i) q^{13} +(-0.770942 - 0.560122i) q^{16} +(0.0388067 - 0.119435i) q^{18} +(-0.263146 - 0.809880i) q^{19} +(1.16089 - 0.843439i) q^{20} +(0.0672897 + 0.106032i) q^{22} -0.851559 q^{23} +(0.347824 + 1.07049i) q^{25} +(0.0751750 - 0.231365i) q^{26} +(-0.866986 + 0.629902i) q^{31} +0.368852 q^{32} +(-0.304144 - 0.936058i) q^{36} +(0.0865160 + 0.0628575i) q^{38} +(-0.112263 + 0.345510i) q^{40} +(0.915113 + 0.362319i) q^{44} +1.45794 q^{45} +(0.0865160 - 0.0628575i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-0.114356 - 0.0830844i) q^{50} +(-0.589177 - 1.81330i) q^{52} +(-0.929324 + 1.12336i) q^{55} +(0.0415873 - 0.127993i) q^{62} +(0.733468 - 0.532896i) q^{64} +2.82427 q^{65} +1.75261 q^{67} +(0.201592 + 0.146465i) q^{72} +(-0.613161 + 1.88711i) q^{73} +0.838129 q^{76} +(-0.809017 + 0.587785i) q^{79} +(0.429324 + 1.32132i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(-0.241353 + 0.0619689i) q^{88} -1.85955 q^{89} +(-0.148122 + 0.107617i) q^{90} +(0.258996 - 0.797108i) q^{92} +(-0.383650 + 1.18075i) q^{95} +(0.303189 - 0.220280i) q^{97} +0.125581 q^{98} +(0.535827 + 0.844328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^4 - 5 * q^9	\( 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} + 15 q^{20} - 5 q^{22} - 5 q^{25} + 15 q^{26} - 10 q^{32} - 5 q^{36} - 10 q^{40} - 5 q^{49} - 10 q^{50} - 10 q^{62} - 5 q^{64} - 10 q^{76} - 5 q^{79} - 10 q^{80} - 5 q^{81} + 15 q^{83} - 5 q^{88} + 15 q^{92} + 15 q^{95}+O(q^{100}) \) 20 * q - 5 * q^4 - 5 * q^9 - 5 * q^16 + 15 * q^20 - 5 * q^22 - 5 * q^25 + 15 * q^26 - 10 * q^32 - 5 * q^36 - 10 * q^40 - 5 * q^49 - 10 * q^50 - 10 * q^62 - 5 * q^64 - 10 * q^76 - 5 * q^79 - 10 * q^80 - 5 * q^81 + 15 * q^83 - 5 * q^88 + 15 * q^92 + 15 * q^95

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